I have a question concerning a double map setup with 4 players (or basically any setup in which one player controls the three sections
of a single map).

I don't know whether I am making this too complicated but I was wondering if it is allowed for any player to attack units that are not on the map that they are playing on i.e. units that are not within the three sectors they are controlling.

I would say it is possible but then again you can never be too sure.
I don't see why I should not be able to help my neighbour with a bit of supporting fire or an air strike even.

In addition to attacking units on a neighboring map, you can move your units onto a neighboring map, and on the next turn they would be controlled by that player. This can be a very useful tactic.

This can be extremely helpful for teammates who are struggling on your Flank! Here's how it works:

Axis Player A wants to help his friend, Axis Player B by sending him a tank unit. The unit is close to the edge, so on his turn, Axis Player A orders the tank unit. The unit moves 3 hexes (one hex on Player A's board, then two hexes on Player B's board). Player A is still in command of the tank and can attack an enemy unit that's in range. After his roll, and any Overrun, the Allies get their turn. When the Axis turn starts back up, Player B is now in command of the tank unit.

I have a question concerning a double map setup with 4 players (or basically any setup in which one player controls the three sections
of a single map).

I don't know whether I am making this too complicated but I was wondering if it is allowed for any player to attack units that are not on the map that they are playing on i.e. units that are not within the three sectors they are controlling.

I would say it is possible but then again you can never be too sure.
I don't see why I should not be able to help my neighbour with a bit of supporting fire or an air strike even.

thanks in advance

Does this mean then, that if I have the BARRAGE card, I may fire on units on the map adjacent to the map I am playing on? Or what about AIRSTRIKE? Or is my assistance to my neighbor limited to my units "crossing the boarder" and attacking?